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Blow-Up and Decay Estimate in a Logarithmic p-Laplace Parabolic Equation LI Ping, LI Feng-jie Chinese Quarterly Journal of Mathematics    2024, 39 (4): 331-354.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.001 Abstract （199）      PDF（pc） （462KB）（101）       Knowledge map    Save This paper deals with an initial-boundary value problem of a fourth-order parabolic equation involving Logarithmic type p-Laplacian, which could be proposed as a model for the epitaxial growth of thin films. By using the variational method and the logarithmic type Sobolev inequality, we give some threshold results for blow-up solutions and global solutions, which could be classified by the initial energy. The asymptotic estimates about blow-up time and decay estimate of weak solutions are obtained. Related Articles | Metrics

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Discontinuous Galerkin Method for Hydrodynamic and Sediment Transport Model ZHANG Ren-peng, WANG Bo, WANG Qiang, Chinese Quarterly Journal of Mathematics    2024, 39 (4): 355-365.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.002 Abstract （91）      PDF（pc） （1085KB）（54）       Knowledge map    Save In this article, we propose and research a first-order, linearized discontinuous Galerkin method for the approximation of the hydrodynamic and sediment transport model. The method is decoupled and fully discrete, and is shown to be unconditionally stable. Furthermore, error estimates are proved. Finally, the theoretical analysis is confirmed by numerical examples. Related Articles | Metrics

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On the Method of Solution for the Non-Homogeneous Generalized Riemann-Hilbert Boundary Value Problems ZHANG Wen-wen, LI Ping-run Chinese Quarterly Journal of Mathematics    2024, 39 (3): 262-269.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.004 Abstract （83）      PDF（pc） （321KB）（40）       Knowledge map    Save This paper studies the non-homogeneous generalized Riemann-Hilbert (RH) problems involving two unknown functions. Using the uniformization theorem, such problems are transformed into the case of homogeneous type. By the theory of classical boundary value problems, we adopt a novel method to obtain the sectionally analytic solutions of problems in strip domains, and analyze the conditions of solvability and properties of solutions in various domains. Related Articles | Metrics

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High Energy Normalized Solutions for the Schrödinger Equations with Exponential Critical Growth ZHANG Xiao-cang, XU Li-ping Chinese Quarterly Journal of Mathematics    2025, 40 (1): 1-19.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.001 Abstract （83）      PDF（pc） （417KB）（33）       Knowledge map    Save In this paper, we study high energy normalized solutions for the following Schrödinger equation …… Related Articles | Metrics

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Combinatorial Identities Concerning Harmonic Numbers CHEN Yu-lei, GUO Dong-wei Chinese Quarterly Journal of Mathematics    2024, 39 (3): 307-314.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.008 Abstract （80）      PDF（pc） （295KB）（55）       Knowledge map    Save In this paper, we firstly establish a combinatorial identity with a free parameter x, and then by means of derivative operation, several summation formulae concerning classical and generalized harmonic numbers, as well as binomial coefficients are derived. Related Articles | Metrics

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Pseudo S-Asymptotically (ω,c)-Periodic Solutions to Fractional Differential Equations of Sobolev Type MAO Hang-ning, CHANG Yong-kui Chinese Quarterly Journal of Mathematics    2024, 39 (3): 295-306.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.007 Abstract （73）      PDF（pc） （402KB）（36）       Knowledge map    Save In this paper, we firstly recall some basic results on pseudo S-asymptotically (ω,c)-periodic functions and Sobolev type fractional differential equation. We secondly investigate some existence of pseudo S-asymptotically (ω,c)-periodic solutions for a semilinear fractional differential equations of Sobolev type. We finally present a simple example. Related Articles | Metrics

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Italian Domination of Strong Product of Two Paths WEI Li-yang, LI Feng Chinese Quarterly Journal of Mathematics    2024, 39 (3): 221-234.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.001 Abstract （68）      PDF（pc） （392KB）（50）       Knowledge map    Save The domination problem of graphs is an important issue in the field of graph theory. This paper mainly considers the Italian domination number of the strong product between two paths. By constructing recursive Italian dominating functions, the upper bound of its Italian domination number is obtained, and then a partition method is proposed to prove its lower bound. Finally, this paper yields a sharp bound for the Italian domination number of the strong product of paths. Related Articles | Metrics

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Normalized Ground State Solutions of Nonlinear Choquard Equations with Nonconstant Potential LI Nan, ZHAO Hui-yan, XU Li-ping Chinese Quarterly Journal of Mathematics    2024, 39 (3): 250-261.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.003 Abstract （65）      PDF（pc） （425KB）（34）       Knowledge map    Save  In this paper, we mainly focus on the following Choquard equation...... Related Articles | Metrics

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Fekete-Szegö Inequalities and the Symmetric Toeplitz Determinants for Certain Analytic Function Class Involving q-Differintegral Operator PEI Ke-ke, LONG Pin-hong, LIU Jin-lin, GANGADHARAN Murugusundaramoorthy Chinese Quarterly Journal of Mathematics    2024, 39 (4): 366-378.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.003 Abstract （64）      PDF（pc） （387KB）（74）       Knowledge map    Save In this paper, we introduce and investigate certain subclass of analytic and univalent functions involving q-differintegral operator. For this function class, we give the bound estimates of the coefficients a2 and a3 and some Fekete-Szegö functional inequalities. Besides, we also estimate the corresponding symmetric Toeplitz determinants. Furthermore, we point out some consequences and connections to these results above. Related Articles | Metrics

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The Varieties of Semi-Conformal Vectors of Rank-One Even Lattice Vertex Operator Algebras CHU Yan-jun, GAO Yi-bo Chinese Quarterly Journal of Mathematics    2025, 40 (1): 36-48.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.004 Abstract （63）      PDF（pc） （430KB）（26）       Knowledge map    Save In this paper, we shall study structures of even lattice vertex operator algebras by using the geometry of the varieties of their semi-conformal vectors. We first give the varieties of semi-conformal vectors of a family of vertex operator algebras…… Related Articles | Metrics

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The Hyers-Ulam Stability and Hyers-Ulam Instability for Some Nonhomogeneous Ordinary Differential Equations DENG Jing-tao Chinese Quarterly Journal of Mathematics    2024, 39 (4): 420-430.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.008 Abstract （59）      PDF（pc） （341KB）（43）       Knowledge map    Save In this paper, we get a necessary and sufficient condition such that a class of differential inequalities hold. Using this necessary and sufficient condition, we prove that a class of first order nonhomogeneous ordinary differential equations have the Hyers-Ulam stability. And then, we prove that some first order nonhomogeneous ordinary differential equations and some second order nonhomogeneous ordinary differential equations do not have the Hyers-Ulam instability under some suitable conditions. Related Articles | Metrics

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The Existence of Solutions for Kirchhoff-Type Equations with General Singular Terms WANG Ji-nan, SUN Da-wei Chinese Quarterly Journal of Mathematics    2024, 39 (3): 315-323.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.009 Abstract （59）      PDF（pc） （314KB）（30）       Knowledge map    Save We study the existence of solutions for Kirchhoff-type equations. Firstly, we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global minimum. Then, we use the variational method and some analytical techniques to obtain the existence of the positive solution of the equation when λ is small enough. Related Articles | Metrics

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On the Weyl’s Lemma for Triharmonic Functions ZHENG Run-jie, ZENG Jia-min, FANG Yi Chinese Quarterly Journal of Mathematics    2024, 39 (3): 288-294.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.006 Abstract （52）      PDF（pc） （271KB）（52）       Knowledge map    Save In this paper, by choosing some appropriate test functions, we prove the Weyl’s lemma for triharmonic functions based on the new type of mean value formulas. Related Articles | Metrics

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A Remark on the Affine Coordinates for KdV Tau-Functions FU Zhi-peng Chinese Quarterly Journal of Mathematics    2024, 39 (3): 324-330.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.010 Abstract （51）      PDF（pc） （259KB）（21）       Knowledge map    Save We give a proof of an explicit formula for affine coodinates of points in the Sato’s infinite Grassmannian corresponding to tau-functions for the KdV hierarchy. Related Articles | Metrics

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Ostrowski’s Type Inequalities for Generalized (h,m)−Preinvex Functions with Its Applications LI Ran, LIAN Tie-yan Chinese Quarterly Journal of Mathematics    2024, 39 (3): 270-287.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.005 Abstract （49）      PDF（pc） （420KB）（23）       Knowledge map    Save A new concept generalized (h,m)−preinvex function on Yang’s fractal sets is proposed. Some Ostrowski’s type inequalities with two parameters for generalized (h,m)−preinvex function are established, where three local fractional inequalities involving generalized midpoint type, trapezoid type and Simpson type are derived as consequences. Furthermore, as some applications, special means inequalities and numerical quadratures for local fractional integrals are discussed. Related Articles | Metrics

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Factorized Smith Method for A Class of High-Ranked Large-Scale T-Stein Equations LI Xiang, YU Bo, TANG Qiong Chinese Quarterly Journal of Mathematics    2024, 39 (3): 235-249.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.002 Abstract （48）      PDF（pc） （11638KB）（63）       Knowledge map    Save We introduce a factorized Smith method (FSM) for solving large-scale highranked J-Stein equations within the banded-plus-low-rank structure framework. To effectively reduce both computational complexity and storage requirements, we develop techniques including deflation and shift, partial truncation and compression, as well as redesign the residual computation and termination condition. Numerical examples demonstrate that the FSM outperforms the Smith method implemented with a hierarchical HODLR structured toolkit in terms of CPU time. Related Articles | Metrics

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Branch and Bound Algorithm for Globally Solving Minimax Linear Fractional Programming WANG Hui-man, SHEN Pei-ping, LIANG Yu-xin Chinese Quarterly Journal of Mathematics    2024, 39 (4): 388-398.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.005 Abstract （45）      PDF（pc） （344KB）（21）       Knowledge map    Save In this paper, we study the minimax linear fractional programming problem on a non-empty bounded set, called problem (MLFP), and we design a branch and bound algorithm to find a globally optimal solution of (MLFP). Firstly, we convert the problem (MLFP) to a problem (EP2) that is equivalent to it. Secondly, by applying the convex relaxation technique to problem (EP2), a convex quadratic relaxation problem (CQRP) is obtained. Then, the overall framework of the algorithm is given and its convergence is proved, the worst-case iteration number is also estimated. Finally, experimental data are listed to illustrate the effectiveness of the algorithm. Related Articles | Metrics

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The w-(b,c)-Core Inverse FANG Li, ZHAO Liang Chinese Quarterly Journal of Mathematics    2025, 40 (1): 26-35.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.003 Abstract （42）      PDF（pc） （308KB）（24）       Knowledge map    Save We introduce and study a new kind of generalized inverses named w-(b,c)-core inverses, which is a generalization of the (b,c)-core inverse. An example is given to show that w-(b,c)-core inverses need not be (b,c)-core inverses. In addition, the dual version of the w-(b,c)-core inverse is studied. Some results on (b,c)-core inverses and e-(b,c)-core inverses are unified and generalized. Related Articles | Metrics

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The Degree of Approximation by (E,q)(C,α,β) Means in Orlicz Spaces CHEN Lin, WU Ga-ridi Chinese Quarterly Journal of Mathematics    2024, 39 (4): 399-406.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.006 Abstract （40）      PDF（pc） （360KB）（16）       Knowledge map    Save In this paper, we study the trigonometric approximation problems of functions which belong to the Lipα class, the Lip(ξ(t)) class, and the W(L∗M;ξ(t)) class in Orlicz spaces by using the tools Hölder inequality in Orlicz spaces, the second mean value theorem for integrals, and (E,q)(C,α,β) means etc. At the same time, we give the corresponding degree of approximation. Related Articles | Metrics

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Independence Polynomials and the Merrifield-Simmons Index of Mono-Layer Cylindrical Grid Graphs JI Lin-xing, ZHANG Ke, HU Wen-jun Chinese Quarterly Journal of Mathematics    2024, 39 (4): 379-387.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.004 Abstract （40）      PDF（pc） （490KB）（84）       Knowledge map    Save Research on the independence polynomial of graphs has been very active. However, the computational complexity of determining independence polynomials for general graphs remains NP-hard. Let α(G) be the independence number of G and i(G; k) be the number of independent sets of order k in G, then the independence polynomial is defined as ...... Related Articles | Metrics